A circle of interacting servers; spontaneous collective behavior in case of large fluctuations

TL;DR

This paper analyzes how large fluctuations cause overloads in a circular network of servers with dynamic routing, revealing a critical input rate where all servers are most likely to overload.

Contribution

It introduces a model of server overloads in a circular network with dynamic routing and identifies a critical input rate leading to collective overload behavior.

Findings

Existence of a critical input rate for overloads

Most probable overload of all servers occurs above this rate

Overload probability depends on input flow rate

Abstract

We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed between two neighboring servers, upon its arrival a message is directed to the least loaded of these servers. Under the condition that at least two servers are overloaded the number of overloaded servers in such network depends on the rate of input flows. In particular there exists critical level of input rate that in case of higher rate most probable that all servers are overloaded.